from itertools import pairwise
from math import sqrt
from typing import *
from sortedcontainers import SortedList


class Solution:

    def gcdSort(self, nums: List[int]) -> bool:
        mx = max(nums)


        p = [v for v in range(mx + 1)]

        def find(a):
            if p[a] != a:
                p[a] = find(p[a])
            return p[a]

        def union(a, b):
            A, B = find(a), find(b)
            p[A] = B
        mx = max(nums)
        is_prime = [True] * (mx + 1)
        s = set(nums)
        for num in range(2,mx + 1):
            if is_prime[num]:
                for i in range(num,mx+1,num):
                    is_prime[i] = False
                    if i in s:
                        union(i,num)
            
        st = sorted(nums)
        for a, b in zip(st, nums):
            if find(a) != find(b):
                return False
        return True


so = Solution()
print(so.gcdSort(nums=[7, 21, 3]))
print(so.gcdSort(nums=[5, 2, 6, 2]))
print(so.gcdSort(nums=[10, 5, 9, 3, 15]))
def gcdSort(a):
    pass
print(
    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))

# sd = SortedList()
# sd.add(30)
# sd.add(15)
# sd.add(50)
# print(sd)


# def primes(ceil):
#     is_prime = [True] * (ceil + 1)
#     primes = []
#     for num in range(2, ceil + 1):
#         if is_prime[num]:
#             primes.append(num)
#         for prime in primes:
#             if num * prime > ceil:
#                 break
#             is_prime[num * prime] = False
#             if num % prime == 0:
#                 break
#     return primes


# def factors(ceil: int):
#     prime_list = primes(ceil)
#     factors = DefaultDict(list)
#     for num in range(2, ceil + 1):
#         enum = num
#         for prime in prime_list:
#             if enum == 1 or prime > enum:
#                 break
#             cnt = 0
#             while enum % prime == 0:
#                 cnt += 1
#                 enum //= prime
#             if cnt > 0:
#                 factors[num].append([prime, cnt])
#     return factors


# factors_list = factors(500)
# for num in [47, 431]:
#     factor = factors_list[num]
#     print(num, end=' -> ')
#     for k, v in factor:
#         print(f"{k}:{v}", end=',')
#     print(' ')


# class Solution:

#     def gcdSort(self, nums: List[int]) -> bool:

#         def find(x):
#             if f[x] != x:
#                 f[x] = find(f[x])
#             return f[x]

#         def union(x, y):
#             f[find(x)] = find(y)

#         M, vis = max(nums) + 1, set(nums)
#         f, flags = list(range(M)), [1] * M
#         for p in range(2, M):
#             if flags[p]:
#                 for x in range(p * 2, M, p):
#                     flags[x] = 0
#                     if x in vis:
#                         union(x, p)
#         res = True
#         nums1 = sorted(nums)
#         n = len(nums)

#         for i in range(n):
#             if nums[i] != nums1[i] and find(nums[i]) != find(nums1[i]):
#                 res = False
#                 break
#         return res

# class PrimeFactor:

#     def __init__(self, ceil):
#         self.ceil = ceil  # 上限
#         self.prime_factor = [[] for _ in range(self.ceil + 1)]  # 因数列表
#         self.min_prime = [0] * (self.ceil + 1)  # 最小因数
#         self.primes = []
#         self.init_prime_factor()
#         return

#     def init_min_primes(self):
#         # 模板：计算 1 到 self.ceil 所有数字的最小质数因子 min_prime
#         # 模板: 收集 1 到 self.ceil 所有质数
#         for i in range(2, self.ceil + 1):
#             if not self.min_prime[i]:
#                 self.min_prime[i] = i
#                 self.primes.append(i)
#             for j in range(i * i, self.ceil + 1, i):
#                 if self.min_prime[j] == 0:
#                     self.min_prime[j] = i
#             for p in self.primes:
#                 if i * p > self.ceil:
#                     break
#                 self.min_prime[i * p] = p
#                 if i % p == 0:
#                     break

#     def init_prime_factor(self):
#         self.init_min_primes()
#         # 模板：计算 1 到 self.ceil 所有数字的质数分解（可选）
#         for num in range(2, self.ceil + 1):
#             i = num
#             while num > 1:
#                 p = self.min_prime[num]
#                 cnt = 0
#                 while num % p == 0:
#                     num //= p
#                     cnt += 1
#                 self.prime_factor[i].append([p, cnt])
#         return

# a = PrimeFactor(10000)
# # print(a.prime_factor[7171])
# print(a.prime_factor[9795])

